Anyways, I feel I know better about limits technique during proving, rather than just memorize the definitions and try to squeeze them out. Well, the metaphor is bizarre but you know what I mean...Now I'm more familiar with the usage, or the whole idea of proving a big-Oh, a big-Omega and a big-Theta. However, I'm still little confused about halting problems. While doing the assignment, I did not understand how reductions help prove whether a function is un-computable or not. Luckily, there was some guy sharing his confusion about halting problems on Piazza. The part of Larry's answer helped:
This final week we only introduced two new concepts: countability and induction. Since I took linear algebra last semester, the concepts of mapping, one-to-one and onto are no strangers to me.
Here is an example of proving |X|=|Y| where X={natural numbers}and Y={even natural numbers}.
The key of tacking that would be showing f is well-defined, 1-1, onto step by step.
(Remember to check indention)
However, the Truth-Table of showing fx() cannot be programmed confused me a great deal.I'm plannig to go to the office hour.
Also, I learnt induction while doing math proofs on Calculus class. The main structure is to first assume a base case and then start the inductive steps(n => n+1).
Additionally, I really appreciate "Review for final" part Larry summarized for us.It tells us that which parts of course materials are more likely to be tested, like a list high-lighting all the important concepts of the course.
Last, I thanked Yahui and Timothy by commenting on their last post. http://timothylock.me/sLOG/2014/11/30/week-11-halting/#comment-8
While browsing their Week 12 slogs, I found there were other students commenting "Thanks" as well, so my sense of picking slogs is seemingly pretty good~
Well, finally the semester ended. I would say I really enjoyed this course and loved the creative teaching style of my instructor, Prof Larry Zhang. Definitely, I would recommend csc165 to my friends. Now it's time to say: good luck to the final!